II see, the Pope doesn't get that much science. But I was thinking for a low cost mission to Neptune, that's why it's launched on a Neptune 1B, not a Jarvis. However, the kick motor does sound quite a bit promising, so how about making this Neptune atmospheric probe (Okay, saying "Neptune atmospheric probe" is a bit of a mouthful, so I'll just call it NAP for now until we get a proper name) say, 150 kg to have a larger science package? Or maybe 180 kg?
Understandable. So, let's try to make up this mission on a Neptune-1B!
A 150 kg probe, for me, can carry something as same science package but being more pressure-resistant, or vice versa can have the same resistence and a pair or three more instruments.
For comparison, the 300 kg Efesto (i'm talking of the overall weight of probe+aeroshell) carries eight instruments: camera, IR radiometer, nephelometer, lightning detector, net flux radiometer, temperature and pressure probe, anemometer, mass spectrometer.
Also, how much do you think the cruise stage would weigh? Keep in mind it needs these things:
RTGs for power
Medium/High gain comm. dishes for communication with Earth
Low gain antennae for communications with the NAP
RCS control thrusters for changing attitude
Separation mechanism for the NAP
Camera(s) for both navigation and taking pictures of Neptune to try to make an accurate global map
Neptune science package/equipment
And probably a whole bunch of other stuff which I can't think of off the top of my head.
It's difficult to answer; ideally, for a light cruse stage, at least the science package must be scrapped almost entirely, saving at least some dozens of kilograms. And the cameras are often the heaviest payloads...
I think that even a minimal cruise stage can weigh about the same of the atmospheric probe. For reference, Pioneer Venus 2 weighs 270 kg, and the Large Probe circa 315.
EDIT: How much would adding payload would adding a kick motor on top of the Fregat (I assume the 2nd stage will do some of the burn, the Fregat will do some perigee passes while burning, and then the kick motor will do the final kick to Jupiter), say perhaps a Star 48B add to the payload to TJI?
A Neptune-1B with a Star 48B fourth stage can put about 800-900 kg on the required 7,07 km/sec injection burn (depending on the security margin that you want assume - the 900 kg option has virtually no margin).